{
  "id": "1001.4360",
  "version": "v1",
  "published": "2010-01-25T09:54:59.000Z",
  "updated": "2010-01-25T09:54:59.000Z",
  "title": "The cluster character for cyclic quivers",
  "authors": [
    "Ming Ding",
    "Fan Xu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We define an analogue of the Caldero-Chapoton map (\\cite{CC}) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character (in the sense of \\cite{Palu}) and satisfies some inductive formulas for the multiplication between the generalized cluster variables (the images of objects of the cluster category under the map). Moreover, we construct a $\\mathbb{Z}$-basis for the algebras generated by all generalized cluster variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-25T09:54:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G20"
    ],
    "keywords": [
      "cluster character",
      "cyclic quiver",
      "generalized cluster variables",
      "finite dimensional nilpotent representations",
      "cluster category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}